Meta-prompt ESR enhancement effects scale with model size across Llama and Gemma families

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• Meta-prompting increases Llama-3.3-70B multi-attempt rate 4.3× (from 7.4% to 31.7%)finding0.786
  Demonstrates ESR can be deliberately enhanced through prompting in the largest model
• Meta-Prompting for ESR Enhancementmethod0.781
  Appending instructional meta-prompts to object-level prompts to deliberately enhance ESR in models
• All five judge models consistently rank Llama-3.3-70B as having substantially higher ESR rates than other modelsfinding0.775
  Cross-judge validation of the primary ESR finding across OpenAI, Alibaba, Anthropic, and Google judge models
• ESR exhibits non-monotonic relationship with boost level, peaking around -0.3σ below threshold in Llama-3.3-70Bfinding0.775
  Characterizes the narrow operating window in which ESR can manifest
• The generalization improvement from explicit instructions observed in Llama models (A1-A3 to F0-F2) is more pronounced for F3-F5 to F0-F2 in Gemma models.claim0.770
  Shows the instruction effect, while shifting geometry, may not produce consistent generalization effects across model families.
• We cannot isolate whether ESR reflects scale, architecture, or training procedures in Llama-3.3-70Bclaim0.766
  Epistemic limitation claim acknowledging confounds in the cross-model comparison
• The difficulty boundary for truth directions replicates across all four tested models (Llama-3.2-3B, Llama-3.1-8B, Gemma-2-2b, Gemma-2-9b); generalization to F3-F5 remains consistently low regardless of model size or family.finding0.762
  Establishes generalizability of the core difficulty-boundary finding across model families.
• All three Gemma-2 models show ESR rates below 1%, near indistinguishable from zerofinding0.761
  Establishes potential Llama-family specificity or scale specificity of ESR phenomenon